Ratio Definition

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In this section, we learn how to calculate, write, and simplify ratios and rates. A ratio is a comparison of two quantities with the same units. We use three methods to display a ratio: as a fraction, using the word “to”, or with a colon ":". As an example, suppose a recipe calls for two cups of flour for every one cup of sugar. The ratio of flour to sugar is said to be: 2:1. This is extremely useful if we wanted to double or triple the recipe. If we wanted to make three batches, we would multiply each part by three and get six cups of flour and three cups of sugar.
Example 1: A recipe calls for 3 cups of flour and 1 cup of sugar
How much sugar is used to triple the recipe?
• In the original, the ratio was 3:1 - flour:sugar
• To triple the recipe we multiple each part of the ratio by 3 -> 9:3 - flour:sugar
This tells us we need 3 cups of sugar
A rate is a ratio where the units are different. Most often we discuss "unit rates", or the amount of one thing per one unit of another. A good example is miles per gallon of gas. If a car can travel four hundred miles on ten gallons of gas, its fuel economy is 40 miles per gallon of gas. How much of one thing (miles traveled), given a single unit of another (gallons of gasoline).
Example 2: A car drives 200 miles on 8 gallons of gas.
What was the MPG or Miles per gallon for the car?

• We have 200:8 - Miles Driven:Gallons of Gas Used
• We can divide 200 by 8 to get the unit rate: 200 ÷ 8 = 25
The car's MPG was 25 or we could say it got 25 miles to one gallon of gas.
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